Electronic integration apparatus



April 3o, 1968 E. O. GILBERT ETAL.

ELECTRONIC INTEGRATION APPARATUS Original Filed Aug. 27, 1964 2Sheets-Sheet l ATTORNEY April 30, 1968 E, o. GILBERT ETAL 3,381,230

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ABSORP TION AND l INVENTORS A FINITE G IN EDWARD O GILBERT CHARLESH.SINGLE BY IWA/Afm' ATTORNEY United States Patent O 3,381,236ELECTRONIC INTEGRATHN APPARATUS Edward 0. Giibert and Charles H. Single,Ann Arbor, Mich., assignors to Applied Dynamics, Inc., Ann Arbor, Mich.,a corporation of Michigan `Continuation of application Ser. No. 392,439,Aug. 27, 1964. This application Aug. 23, 1966, Ser. No. 574,468 13Claims. (Cl. 328-127) ABSTRACT F THE DISCLSURE An electronic Millerintegrator having an amplifier and a computing capacitor and providedwith a positive feedback network having a transfer function equal to thedifference `between the amplifier-capacitor transfer function and l/p,where p is the differential operator d/dz, with the feedback networkhaving a plurality of RC branches to compensate for absorption in thecomputing capacitor, a resistive branch to compensate for capacitorleakage and amplifier gain limitations, a capacitor-diode branch tocompensate for the voltage coefiicient of the computing capacitor, and asmall capacitor having a large temperature coefficient to compensate forthe temperature coefficient of the computing capacitor, and anadjustable voltage divider connected to apply an input currentseparately from adjustment of the amplifier voltage offset.

This application is a continuation of application Ser. No. 392,489, Aug.27, 1964, and now abandoned.

This invention relates to electronic integrators, and more particularlyto improved electronic integrator circuits having greater accuracy. Inthe analog computer, automatic control and instrumentation art,integration is commonly accomplished by so-called Miller integrators,which comprise operational amplifiers having a feedback capacitorconnected between the amplifier output and input terminals, and one ormore input resistors connected between one or more input signal sourcesand the amplifier input terminal. if `plural input signals are appliedto plural resistor inputs `of such integrators, the integrators sum thesignals as well as integating them with respect to time. lf variousadjustments are made to the operational amplifier to minimize errors dueto voltage offset and current input to the operational amplifier, theaccuracy of integration is usually limited chiefly by thecharacteristics of the feedback capacitor. Because of the computingaccuracies required, the prior art in general has resorted to the use ofexpensive capacitors, usually utilizing a solid dielectric, andfrequently such capacitors have been housed in temperature-controlledenvironmental chambers in order to improve their electricalcharacteristics. Despite such elaborate and expensive measures, thelimitations of the best-availabie computing capacitors have resulted inintegration inaccuracies amounting to a major source of computer dynamicerror.

While the prior art usually has attempted to overcome capacitorlimitations by improvements in capacitor manufacture, the presentinvention, on the other hand, is based on a principle of acknowledgingthe capacitor limitations, and of providing compensating circuitry whichovercomes the effects of such limitations. Thus it is a primary objectof the present invention to provide an improved electronic integratorcircuit having greater computational accuracy.

In the prior art various attempts have been made to compensate forvarious errors caused by integrating capacitor limitations. Oneimportant limitation of highestquality computing capacitors is theirabsorption, or soaking effect, which for a typical polystyrenedielectric ICC resuits in changes of capacitance with frequency of theorder of .02% per decade, and a dissipation factor of about .02%.Consequent computation errors of .03% to 0.1% result in certaintransient solutions. Patent No. 2,745,007, for example, shows the use ofa compensating network following an electronic integrator in an attemptto compensate for capacitor absorption effects. Such circuits sufferfrom the serious disadvantage that their output impedances are high, andfurther from the disadvantage that they are incapable of compensatingfor capacitor leakage resistance or error due to finite amplifier gain.Patent No. 3,047,808 is similar except that it utilizes an absorptioncompensating network preceding the integrator. While it need not havehigh output impedance, that circuit too is incapable of compenasting forerror due to capacitor leakage resistance, fuithermore, the circuit mustbe repeated for each additional input to be summed. The presentinvention overcomes both of these disadvantages, and hence it is anadditional object of the present invention to provide an electronicintegrator circuit compensated for capacitor errors which both have lowoutput impedance and which is compensated for capacitor leakageresistance.

The abovementioned prior art compensation schemes are further inadequatein that they attempt to compensate for capacitor absorption with asingle compensating network. As will :be explained below, pluralcompensating networks are necessary in order to compensate for theeffects of capacitor absorption over a substantial frequency range, andin accordance with the invention, the required compensating networks forabsorption compensating networks for absorption compensation over a widerange of frequencies are easily provided, without lowering the inputimpedance or raising the output irnpedance of the electronic integrator.

General purpose electronic analog computers are used to solve a varietyof problems, and the variety between problems requires that differentnumbers of input si-gnals be applied at different times to be summed andintegrated. if a known number and known types of input signals werealways applied to an integrator circuit, the effects of ampiiflcrvoltage offset and current input on integrator accuracy could beadequately compensated for by conventional balance controls commonlyused with operational amplifiers. The requirements to vary the number ofinput signals, however, has prevented the use of any long termcompensation, or has resulted in many amplifiers having to bere-adjusted very frequently. It is a further object of this invention toprovide electronic Aintegrator circuits incorporating independentvoltage offset and current input balancing means in order that suchintegrator circuits need not be re-adjusted every time their inputsignal configurations are changed.

One of the important limitations of computing capacitors is theirleakage resistance. With non-zero voltage, the greater the leakage ofthe capacitor, the more the integrator circuit will drift or dischargewhen it is intended to be constant. High quality presently-availablecomputing capacitors of 1.0 microfarad capacity have DC leakageresistance of approximately 5 1012 ohms, and such leakage resistance canresult in appreciable computational error. In accordance with thepresent invention, a circuit is provided which compensates for orcancels out error due to leakage, as well as error due to capacitorabsorption effects, and errors due to voltage offsets and currentinputs. Thus it is another object of the invention to provide anelectronic integrator circuit having greater freedom from drift due tocapacitor leakage resistance.

An electronic integrator could integrate theoretically accurately onlyif the gain of its amplifier were infinite, and hence a further errorhas resutled in prior art electonic integrators because the gains oftheir amplifies were necessarily limited. The error due to finiteamplifier gain is similar to that due to capacitor leakage resistance.In accordance with the present invention, a circuit is provided whichmay completely compensate for error due to finite amplifier gain.

Attempts have been made in the prior art to compensate for amplifierfinite gain and capacitor leakage resistance, one such attempt beingshown in Patent No. 3,137,790 issued Iune 16, 1964, to Berry. Such asystem suffers from the disadvantages that it requires at least twoextra amplifiers, that even then the compensation is necessarily onlyapproximate, and that a very large number of additional amplifiers arenecessary if the leakage and finite gain errors are to be substantiallycompletely cancelled. Also, such systems do not compensate in any wayfor capacitor absorption. In accordance with the present invention, theerrors due to leakage resistance and finite gain may be completelycancelled out by the provision of a single simple resistance circuit.Further, by the provision of further simple resistance-capacitancecircuits, errors due to capacitor absorption may be compensated for.

Thus it is a further, and a very important object of the presentinvention, to provide an improved electronic integrator circuit in whichall of the above-mentioned sources of computation error may be simplyand accurately compensated for in a single, reliable and very economicalmanner, thereby to provide an electronic integrator having markedlyimproved accuracy.

The present invention, generally speaking, compensates for a number ofthe errors of the usual electronic integrator by providing, in additionto the usual negative feedback connection through the integrating7capacitor, one or more positive feedback paths through a network havingresistances and capacitances selected according to the integratingcapacitor limitations and the amplifier gain limitation. Such positive`feedback may be provided easily and economically, and adjusted tocompensate for the integrator errors with as great an accuracy as may bedesired.

In its broadest aspects, 4the invention is applicable not only tocompensate for capacitor limitations and amplifier finite gainlimitations, but also for other limitations of the total integratorcircuit. The transfer function of an ideal integrator is l/p. Byproviding positive feedback through a network having an error transferfunction, where the error transfer function is the difference betweenthe actual integrator transfer function and l/p, substantially all ofthe errors of the integrator circuit may be compensated for, includingcharacteristics due to the voltage coeliicient and the temperaturecoefficient of the capacitor.

The invention accordingly comprises the features of construction,combinations of elements, and arrangement of parts, which will beexemplified in the constructions hereinafter set forth, and the scope ofthe invention will be indicated in the claims.

For a fuller understanding of the nature and objects of the invention,reference should be had to the following detailed description .taken inconnection with the accompanying drawing, in which:

FIG. 1 is an elementary electrical yschematic diagram of a prior artelectronic integrator circuit;

FIG. 2 is a theoretical equivalent circuit diagram of the integrator ofFIG. 1, useful in understanding the sources of the computational errorswhich occur in the operation of the integrator of FIG. 1;

QFIG. 3 is an electrical schematic diagram of an improved electronicintegrator constructed in accordance with the present invention; andFIGURES 4, 5, 6A, 6B and 6C illustrate portions of alternativeembodiments of the invention.

The basic prior art electroni-c integrator of FIG. 1 is shown ascomprising operational amplifier A, feedback capacitor C and inputsealing resistors R1 and RZ. Voltages e1 and e2 are assumed to beapplied to resistors R1 and R2, respectively. If the gain of amplifier Ais infinite, and various other characteristics of the amplifier wereperfect, and if capacitor C were a perfect capacitor, an output en fromthe integrator would be in accordance with the following expression:

The actual accuracy is limited, however, by (1) voltage offset in theoperational amplifier, (2) current input to the operational amplifier,(3) capacitor leakage resistance, (4) capacitor absorption, and (5)finite amplifier gain, which has an effect equivalent to that ofcapacitor leakage resistance. Voltage offset in the operationalamplifier has the same effect as an equivalent error in the inputsignais, and in an integrator circuit. such an error obviously isintegrated with respect to time, so that a small voltage offset errorcan result in considerable error in the integrator output voltage ifsuch an integrator input signal is integrated for an appreciable lengthof time. The accuracy of an operational amplifier depends upon the totalcurrent being applied through the input scaling resistors being exactlycancelled by the feedback current and upon no input current tiowing inthe first stage of the amplifier. In order to minimize amplifier inputcurrents, the first stage of some vacuum-tube amplifiers is operated ina starved condition, and in other amplifiers a blocking capacitor isinserted in series with the amplifier input terminal to minimize suchcurrents. Despite such .techniques, small input currents of the order of10-4 microamperes frequently occur and contribute to computationalerror. Like voltage offset, the effect of current input error oncomputation increases with time through integration. The effects whichsuch component limitations have on performance of the overall integratorcircuit may be better understood by reference to the equivalent circuitdiagram of FIG. 2.

In FIG. 2 amplifier A is assumed to be a perfect amplifier, the voltageoffset of the actual amplifier is represented by a small battery sourceof voltage eb, the current input to the actual operational amplifier asi, and the amplifier input impedance to ground is represented by rg. Theactual capacitor C of FIG. 1 is represented within dashed lines in FIG.2 as comprising a basic, or theoretically perfect capacitor C0, togetherwith a plurality of parallel circuits which represent the effects ofvarious limitations of an actual computing capacitor. Resistance RLrepresents capacitor leakage resistance, and resistance RG representsthe effect caused by the actual amplifier gain being less than infinity.The resistance-capacitance combinations of r1, c1, and r2, c2 representabsorption effects of the actual capacitor. More than two such rcbranches are necessary to describe absorption effects over a substantialfrequency range.

In the prior art it has been common to provide an adjustable balancingcontrol to compensate for voltage offset eb or current i or acombination of these. Such balancing controls insert a compensatingvoltage into the operational amplifier. Because integrating error due toamplifier voltage offset depends only upon the number of input resistorsconnected to the integrator and the amplifier input impedance to ground,such balance controls must be frequently readjusted if these two sourcesof error are to be cancelled as the number and sizes of the inputresistors are varied. Such readjustment becomes tedious andtimeconsuming in a computer having many operational amplifiers withvaried input configurations.

In the embodiment of the invention shown in FIG. 3 the basic integratorcircuit again comprises input scaling resistors R1 and R2, amplier A andlcapacitor C, the latter preferably comprising a high quality computingcapacitor, but a capacitor still having the various limitationsmentioned above. The output voltage e0 from amplifier A is applied viaresistance R-4 to the feedback inverted amplifier A-Z having feedbackresistor R-S. Inasmuch as R-4 and R-S are of equal value, inverteramplifier A-2 has unity gain. The remaining circuitry of FIG. 3 isutilized to compensate for the above-mentioned sources of error.

The voltage offset error is minimized in a conventional manner byadjustment of the amplifier A internal balance control, represented bycontrol knob 9. The voltage offset error of inverter amplifier A-2 iscompensated for by a similar balance control in A-2 represented by knob8. Such balance controls commonly comprise a potentiometer lcircuitwhich inserts an opposite-sense voltage into the differential amplifierinput stage of the amplifier to compensate for voltage offset, thedifferential amplifier stage usually also being connected to receive aDC stabilization signal from a conventional modulator amplifierdemodulator channel represented by a simple block STAB in FIG. 3. Avariety of other zero-lever manual adjustment controls are alsowell-known and may be used in integrators which incorporate the presentinvention. See, for example, pages 6-2 et seq. of Control EngineersHandbook, McGraw-Hill, New York, 195 8.

The amplifier A input current error is balanced by an opposite-signcurrent ic, which is applied to the amplifier A summing junction i0 viaresistor R-B from a voltage divider comprising resistors R-A and R-C.The voltage divider is excited by either a plus or minus constantvoltage, depending upon the polarity of the current iC required tocancel the amplifier A input current. Because amplifier input currentsare generally quite small, of the order of 10-1o amperes or less, thegeneration of an accurate opposite-sense c current would require eitheran extremely high resistance R-B, or an extremely small voltage V ifvoltage were connected directly to resistance RB. By use of the voltagedivider comprising resistances R-A and R-C, with the resistance value ofR-C being considerably smaller than that of R-A, a voltage V largeenough to be accurately measured and a resistance R-B small enough to beeasily provided may be utilized. As indicated by the arrow, resistanceR-C may comprise a variable rheostat to allow adjustment for a very longterm input current changes, or for use of the circuit with differentamplifiers.

It is important to note that adjustment of the conventional balancecontrol 9 to cancel out voltage offset is done in FIG. 3 entirelyindependently from the adjustment of the ic current to cancel outamplifier input current. Because these two sources of error arecancelled out by two independent compensating means, the compensation iscorrect for any variety of different input configurations, and theadjustments need not be changed when different numbers of inputresistors are connected to the integrator summing junction to solvedifferent problems. Thus much better drift performance results for allconfigurations without re-adjustment of the controls being required. Inorder to reduce or eliminate error due to capacitor leakage resistance,finite amplifier gain, and capacitor absorption, positive feedback isapplied through an impedance network which simulates the capacitorleakage and absorption characteristics and the amplifier finite gainlimitation.

In order to decrease or cancel out the effect of the leakage resistanceof capacitor C, a positive feedback voltage is applied to the integratorsumming junction l0 via resistor REL. The output Voltage of inverteramplier A-2 is applied to excite a voltage divider comprisingresistances R11, and RSL. The network comprising resistances Rm, R21.,R31, may be made equivalent to the single resistance RL of FIG. 2. Thusan input may be applied to the summing junction via resistance RZL whichis equal in magnitude and opposite in sign to the leakage input due tothe leakage of capacitor C, and hence the effect of the capacitorleakage resistance will be completely cancelled out. In FIG. 2 parallelresistances RL and Rg may be replaced by a single resistance RK (notshown). If the RIL, RzL, RSL network in FIG. 3 is made equivalent tosuch a resistance the positive feedback input signal applied viaresistance R2L will cancel out both the error due to capacitor leakageand the error due to finite amplifier gain. In typical applications, thevalue of the RK resistance is of the order of 5 1O12 ohms; and again avoltage divider (RlL, RZL) is used both to avoid a requirement for suchan extremely high resistor, and to allow accurate adjustment by makingresistance Ra, an adjustable rheostat.

The absorption current Ia in an imperfect, isotropic dielectric is acurrent proportional to the rate of accumulation of electric chargeswithin the dielectric. The rate of accumulation, and hence theabsorption current, decreases with time after any change of thepotential gradient, so that the absorption current is reversible. Theabsorption current Ia resulting from any change of the potentialgradient is a function, f(t), of the time which has elapsed since thechange occurred. The absorption current through a plane surface of thearea A which is perpendicular to the potential gradient is:

ed dE ,in f (t) dt where f(t) must be experimentally determined for agiven dielectric and wherein e is the dielectric constant.

Capacitor absorption is due to polarization effects within the capacitorand has two main properties, i.e., an effective variation in capacitywith frequency, and an outof-phase component of dissipation which alsovaries with frequency. Thus the dielectric constant of a capacitor isactually a complex function:

When expressed in terms of frequency and relaxation time (the timerequired for polarization to form or disappear), the complex dielectricconstant becomes where e0 is the zero frequency or static dielectricconstant, e... is the infinite frequency dielectric constant, and 1-0 isthe relaxation time, which is a function of temperature. Thus theequivalent circuit of an actual capacitor if one wishes to considerabsorption, would appear to consist of an ideal capacitor shunted by aseries resistor-capacitor circuit. Experimental results, however, showthe equivalent circuit to be more complex, requiring a plurality ofcapacitor-resistor combinations shunted across the ideal capacitor,suggesting that an actual capacitor may have a plurality of relaxationtimes, perhaps due to nonhomogeneities in the dielectric. A number oftechniques for experimentally determining equivalent networks torepresent capacitor absorption are known and need not be set forth indetail herein. For example, see ISA Paper No. 18.2.62 entitled,Capacitor Low Frequency Characteristics, published Oct. 16, 1962 by theInstrument Society of America, New York, N.Y., or .the doctoral thesisAn Analysis of Certain Errors in Electronic Differential Analyzers, byPaul C. Dow, Ir., University of Michigan, Ann Arbor, Mich., July 1957,page 93 et seq. The absorption compensation network used may beidentical to that used to represent the capacitor equivalent circuit, orpreferably, as shown, an equivalent network having voltage dividersscaled to allow smaller resistance values and larger capacitors to beused.

In order to cancel out the effects of absorption currents in capacitorC, further positive feedback signals are applied to the summing junctionvia a plurality of further feedback paths, three of which are shown inFIG. 3, through capacitors C1', C2 and C3', and from three to five suchfeedback networks are in general necessary to cancel the absorptioncurrent Ia over the desired frequcncy range. The number of series RCnetworks which one need parallel to provide an equivalent circuit ofgiven accuracy depends entirely upon the frequency range over which onewishes to compensate errors caused by absorption. Because the absorptioncharacteristic of high quality computing capacitors (such as those usingpolystyrene or Teflon dielectrics) is rather uniform, it is frequentlyunnecessary that these feedback networks be made adjustable, but forextreme precision, resistors R31, R32, and R33 may comprise adjustablerheostats. It will be seen that the effect of the absorption current inmain computing capacitor C will be decreased or cancelled out by anequal but opposite current connected to summing junction through thethree parallel positive feedback paths shown. The absorptioncompensation network (neglecting capacitor leakage) will be seen tocomprise a network having a transfer function selected in accordancewith the difference between the actual transfer function of theintegrating capacitor C (omitting the leakage resistance) and thetransfer function of an ideal capacitor. Thus the positive feedbackthrough the absorption compensation network will apply a feedback signalto the amplifier to substantially cancel out the errors which otherwisearise due to capacitor absorption. Only the effects of the errorportions of the integrating capacitor equivalent circuit are cancelledout, providing integration as if the integrating capacitor weretheoretically perfect.

It will be seen that the integrator output e3 present at the outputcircuit of amplifier A-Z in FIG. 3 is desirably presented from a lowimpedance circuit which may be used to drive other circuits directly. Infact, amplifiers A and A-Z provide plus and minus low impedance outputs.Thus amplifiers A and A-2 comprise a bi-polar amplifier, i.e., one whichprovides two output signals of equal magnitude and opposite polarity.While the increased accuracy obtainable with the present invention makestemperature control less necessary, the relaxation time or times of thecapacitor dielectric are a function of temperature, as mentioned above,and because the temperature coefiicient of the capacitor is not removedor compensated by the present invention, temperature control is stilladvantageous.

While resistances R-4 and R5 are shown as equal resistances, so thatinverting amplifier A-2 has unity gain, it should be noted that othervalues of gain (either greater or less than unity) may be provided withappropriate scaling changes in the compensating positive feedbacknetworks. For example, if resistance R4 were halved, giving amplifierA-2 a gain of 2.0 voltage divider resistors R3L, R31, R32 and R33 shouldbe halved, and the factor of 2.0 scaling thereafter kept in mind if thecircuit output is taken from amplifier A-2.

While FIG. 3 shows the use of an additional amplier A-2 to provide apositive feedback voltage, it also is within the scope of the inventionto provide the necessary positive feedback voltage by other known means.For example, basic amplifier A usually will comprise a plurality ofstages, and, if desired, the positive feedback voltage required toexcite the four voltage dividers shown connected to line 12 in FIG. 3sometimes may be conveniently obtained internally from within amplifierA. Such an arrangement is illustrated in FIG. 4, wherein the basicamplifier (corresponding to A in FIG. 3) is assumed to comprise threeinverting stages, and the positive feedback voltage is shown derivedfrom the second stage. In such an arrangement, of course, thecompensating circuit values must be altered to take into account thesmaller voltage derived from the second stage of the amplifier, in orderthat the same compensating currents be applied to the input summingjunction.

While FIGS. 3 and 4 show the compensating signals being applied to theinput summing junction of the operational amplifiers, it also is withinthe scope of the invention to otherwise apply the positive feedbackcompensating signals. In FIG. 5 the first stage of the operationalamplifier is shown as comprising a conventional differential amplifierhaving two separate input lines, and as above, the second and thirdstages are assumed to invert. differential input stages are commonlyprovided in dual channel amplifiers in order that the DC level or driftcorrection signal from the stabilization amplifier (STAB) channel may beintroduced into the main amplifie-r channel. As shown in FIG. 5, thecompensating signals from the compensating networks may be applied tothe differential amplifier second input line, thereby resulting inpositive feedback. As will now be apparent, the leakage compensationnetwork may be connected in accordance with one of the above-describedpositive feedback connections while the absorption compensation networkis connected in accordance with a different one of the positive feedbackconnection-s, if desired.

Furthermore, while the absorption compensation network has been shown inFIG. 3 as comprising a plurality of parallel-connected branches eachincluding a capacitor and a resistance, various equivalent circuits willbe readily apparent to those skilled in the art as a result of thisdisclosure. For example, the amplifier voltage utilized to drive thecompensating network may be applied directly to a voltage divider (R-61,R-6VZ, R-63, R39, R70) as shown in FIG. 6a, or instead to a secondvoltage divider (l-66, R-67, R-68) from a first voltage divider (l-64,R-65) as shown in FIG. 6b. It should be clearly understood that thoughnot shown, that conventional stabilizing channels may be used with thearrangements of FIGS. 4, 6a and 6b, and that the current inputcompensation circuit (R-A, R-B, R-C) and separate voltage offset balancecontrols (8, 9) of FIG. 3 may be used as well with the arrangementsshown in FIGS. 4, 5, 6a and 6b. Also, it should be noted that theinvention is applicable as well to integrators utilizing single-channelor unstabilized amplifiers as well as the more usual stabilizedamplifiers.

While the invention has been described in connection with capacitorabsorption and leakage compensation and amplifie-r finite gaincompensation, it is important to note that further integrator errors maybe compensated for by provision of further elements in the positivefeedback network, so that the positive feedback network has an errortransfer function as close as possible to the difference between theuncompensated integrator transfer function and 1/ p, the transferfunction of an ideal integrator. In order to compensate for thecomputing capacitor temperature coefficient a further parallel bnanch(not shown) may be provided in the positive feedback network, with suchfurther branch comprising a small capacitor chosen to have a hightemperature coefiicient. For example, if a 1.0 mfd. computing capacitorwere ordinarily used to provide a given time constant, one may insteaduse a 1.01 mfd. capacitor and provide a .O1 mfd. capacitor having a muchhigher times) temperature coefficient in the positive feedback network.The capacity of the large computing capacitor then will be seen to begreater than that of the small compensating capacitor by the same factorn* as that by which the temperature coefficient of the small capacitorexceeds that of the large computing capacitor, where the selectedconstant n equals 100 in the example given. At a reference temperaturethe capacities of the two capacitors will subtract to provide thedesired overall time constant. As the temperature varies, the highpercentage variation in the small capacitor will cancel out the lowpercentage variation of the large capacitor. In order to compensate forcapacitor voltage coefficient, one may use a further small capacitorhaving a large voltage coefiicient (such las a well-known varicap orvoltagesensitive capacitor) in similar manner in the positive feedbacknetwork, again choosing the main computing capacitor size so as tocancel out the capacity of the added voltage-sensitive capacitor at areference temperature. A small capacitor which has sufiiciently hightemperature cocfiicient and voltage coefficient could be used for bothtemperature compensation and voltage coefficient compensation. Ratherthan using a voltage-variablev capacitor in the positive feedbacknetwork, one may instead apply the positive feedback voltage to avoltage divider, and then to a capacitor having a normal voltagecoefficient through a pair of oppositely-poled diodes connected inparallel, so that the increase in capacity orf the diodes as the voltageapplied to them increases in either direction compensates out thevoltage coefficient of the mlain computing capacitor. Such anarrangement is disclosed in FIG. 6c.

The remarkable improvement in integration obtained by the presentinvention is illustrated by the following comparison between the bestpresently-available prior art electronic integrators and one embodimentof the present invention.

Drift less than 10p volts/second over entire computer range (i100 volts)for integrator using 1.0 fd.

Drift ranging from 67p volts/ second at zero volts to 120g volts/secondat i100 volts, for

capacitor. iitegrator using 1.0 fd. capaci or. Effective D.C. leakagegreater than )(1012 ohms.

() ohms.

2X104 for frequencies below 200 c.p.s.

0.02% per decade.

Alfcomloined errors (worst case 0.1

transient and history conditions) within 0,01%,

The aboveelisted performance characteristics 'for one specificembodiment of the invention are biased on an example using a polystyrenecapacitor wherein the absorption compensation networks were separated byfrequency factors of about 30. Theoretically there is no limit to theperfection with which dissipation factor cancellation may be performed.By using a greater number of RC circuits, separated by frequency factorsof approximately 10, for example, the effective polystyrene capacitordissipation factor may be reduced to a factor of approximately 105.

It will thus be seen that we lhave provided an improved electronicintegrator capable of unprecedented long-term stability and accuracy.

It will thus be seen that the objects set for above, among those madeapparent from the preceding description, are eiiiciently attained, andsince certain changes may be made in the above constructions withoutdeparting from the scope of the invent-ion, it is intended that allmatter contained or shown in the accompanying drawings shall beinterpreted as illustrative and not in a limiting sense.

Having described our invention, what we claim as new and desire tosecure by Letters Patent is:

1. An electronic integrator circuit, comprising, in combination: firstand second electronic amplifiers each having an input terminal, anoutput terminal and inverting amplifying means connected between saidterminals, the input terminal of said first amplifier being adapted -toreceive an input signal; a first capacitor connected between the inputand output terminalsof said first amplifier, thereby providing an ouputsignal at the output terminal of said first amplifier commensurate withthe time integral of said inrput signal, said capacitor having leakageresistance; a resistive first feedback impedance means connected betweenthe input and output terminals of said second amplifier; circuit meansfor connecting the output terminal of said first amplifier to the inputterminal of said second amplifier; and a second feedback impedance meansconnected between the output terminal of said second amplifier and theinput terminal of said first amplifier, said second feedback impedancemeans comprising first resistance means having a resistancesubstantially commensurate with said leakage resistance of said firstcapacitor.

2. An electronic integrator circuit, comprising, in combination: firstyand second electronic amplifiers each having an input terminal, anoutput terminal and inverting amplifying means connected between saidterminals, the input terminal of said :first amplifier being adapted toreceive an input signal; a first capacitor connected between the inputand output terminals of said first amplifier, thereby providing anoutput signal at the output terminal of said first amplifiercommensurate with the time integral of said input signal, said capacitorhaving a dielectric absorption characteristic; a resistive firstfeedback impedance means connected between the input and outputterminals of said second amplifier; circuit means for connecting theoutput terminal of said first amplifier to the input terminal of saidsecond amplifier; and a second feedback impedance means connectedbetween the output terminal of said second amplifier and the inputterminal of said first amplifier, said second feedback impedance meanscomprising a plurality of resistance-capacitance circuit branchesconnected between said output terminal of said second amplifier and saidinput terminal of said first amplifier, said resistance-capacitancecircuit branches having a transfer function commensurate with thetransfer function of said dielectric absorption characteristic of saidfirst capacitor.

3. An electronic integrator circuit, comprising, in combination: anelectronic amplifier having an input terminal, an output terminal, and aplurality of amplifier stages connected between said terminals, saidplurality of amplifier stages collectively providing an overall polarityinversion between said terminals, a first capacitor having a selectedcapacity connected between said terminals; an inverting amplifier meansconnected to invert the signal at said output terminal to provide afurther signal; and an impedance network for connecting said furthersignal to said input terminal, said impedance network having a transferfunction commensurate with the difference between the transfer functionbetween said input and output terminals and a transfer function valuel/p of an ideal capacitor having said selected capacity, where p is thedifferential operator d/dt.

4. An integrator circuit according to claim 1 in which said secondamplifier has unity negative gain.

5. An integrator circuit according to claim 1 in which said rstresistance means comprises a voltage divider connected to said outputterminal of said second amplifier, said voltage divider having a tapterminal, and a resistor connected between said tap terminal and saidinput terminal of said first amplifier.

6. An integrator circuit according to claim 2 in which said secondfeedback impedance means comprises voltage divider means connected tosaid output terminal of said seco-nd amplifier, said voltage dividermeans having a plurality of tap terminals, and a plurality ofcapacitanceY rneans connected between respective tap terminals and saidinput terminal of said first amplifier.

'7. An integrator circuit according to claim 2 in which at least one ofsaid circuit branches comprises a voltage divider connected to theoutput terminal of said second amplifier, said voltage divider having atap terminal, and a resist-or and a second capacitor connected in seriesbetween said tap terminal and said input terminal of said firstamplifier.

8. An integrator circuit according to claim 3 in which said impedancenetwork comprises a second capacitor, said first capacitor having acapacity which is n times the capacity of said second capacitor, saidsecond capacitor having a temperature coefficient which is substantiallyn times the temperature coefiicient of said rst capacitor, where n is aselected constant.

9. An integrator circuit according to claim 3 in which said impedancenetwork comprises a second capacitor, said first capacitor having acapacity which is n times the capacity of said second capacitor, saidsecond capacitor having a voltage coefficient which is substantially ntimes the voltage coefficient of said first capacitor, where n is aselected constant.

10. An integrator circuit according to claim 3 in which said impedancenetwork comprises a second capacitor, said first capacitor having acapacity which is n times the capacity of said second capacitor, saidsecond capacitor having voltage and temperature coefficients each ofwhich are substantially n times the voltage and temperature coefficientsof said first capacitor, where n is a selected constant.

11. An integrator circuit according to claim 1 in which said secondfeedback impedance means comprises a voltage divider connected to saidoutput terminal of said second amplifier, said voltage divider having atap terminal, a second capacitor, and a pair of oppositely poled diodesconnected in parallel with each other, said second capacitor and saidpair of diodes being connected in series between said tap terminal andsaid input terminal of said first amplifier.

12. An integrator circuit according to claim 1 in which said firstamplifier includes a differential amplifier stage having first andsecond input circuits, said first input circuit being connected to saidinput terminal of said first amplifier; and a stabilizer amplifierchannel connected between said first and second input circuits of saiddifferential amplifier stage.

13. An integrator circuit according to claim 1 in which said firstamplifier includes a differential amplifier stage having first andsecond input circuits, said first input circuit being connected to saidinput terminal of said first amplifier; first adjustable means forapplying a selected input voltage to said second input circuit; andsecond adjustable means for applying a selected input current to saidfirst input circuit, said second adjustable means comprising a pair ofsources of fixed voltage of opposite polarity, an adjustable voltagedivider, switch means for connecting said voltage divider to be excitedby a selected one of said sources of fixed voltage, and a resistanceconnected between said voltage divider and said input terminal of saidfirst amplifier.

References Cited UNITED STATES PATENTS 7/1962 Thompson 328-162 X 1/1965Davis et al. 328-127 OTHER REFERENCES ARTHUR GAUSS, Primary Examiner.

I. ZAZWORSKY, Assistant Examiner.

